Optimal scaling of random walk Metropolis algorithms using Bayesian large-sample asymptotics

High-dimensional asymptotics have been shown to be useful to derive tuning rules for finding the optimal scaling in random walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive; the target density is typically assumed to be of a product form. Users may thus doubt the validity of such tuning rules in practical applications. In this paper, we shed some light on optimal scaling problems from a different perspective, namely a large-sample one. This allows to prove weak convergence results under realistic assumptions and to propose novel parameter dimension dependent tuning guidelines. The proposed guidelines are consistent with previous ones when the target density is close to having a product form, but significantly different when this is not the case.